Numerical Methods for Parameter Estimation in Nonlinear Differential Algebraic Equations

Abstract

MSC (2000) 49M37,65K10,65L10,65L80,90C06,90C30Nonlinear Differential Algebraic Equations (DAEs) are an important class of models for dynamic processes. To establish models that describe the process behavior in a quantitatvely correct way, often parameters in the model have to be determined from observations or measurements of the process. This paper reviews numerical methods for parameter estimation in DAEs. In particular the so-called boundary value problem approach and a versatile realisation, the multiple shooting method for parameter estimation, are discussed. Several applications are given to show the numerical performance and the wide applicability of the methods. A difficulty that occurs in practical applications is that the experiments performed to obtain measurements for parameter estimation are expensive, but nevertheless do not guarantee satisfactory parameter accuracy. The optimization of one or more dynamic experiments in order to maximize the accuracy of the results of a parameter estimation subject to cost and further technical inequality constraints leads to very complex non-standard optimal control problems. Newly developed methods for design of optimal experiments for nonlinear processes are briefly discussed.

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